%0 Journal Article
%T Synchronization of Uncertain Fractional-Order Hyperchaotic Systems via Unidirectional Linear Error Feedback Coupling Scheme
%A Suwat Kuntanapreeda
%J Journal of Chaos
%D 2013
%R 10.1155/2013/512403
%X A simple method for synchronization of uncertain fractional-order hyperchaotic systems is proposed in this paper. The method makes use of a unidirectional linear coupling approach due to its simple configuration and ease of implementation. To determine the coupling parameters, the synchronization error dynamics is first formulated as a fractional-order linear interval system. Then, the parameters are obtained by solving a linear matrix inequality (LMI) stability condition for stabilization of fractional-order linear interval systems. Thanks to the existence of an LMI solution, the convergence of the synchronization errors is guaranteed. The effectiveness of the proposed method is numerically illustrated by the uncertain fractional-order hyperchaotic Lorenz system. 1. Introduction Chaos synchronization has attracted great attention due to its superior potential applications, for example, in communication and optics. It has been studied since the pioneering work of Pecora and Carroll [1] was published. Currently, studies of chaos control and synchronization have more focus on hyperchaotic systems because of their rich chaos behaviors. Although the notion of fractional calculus dates from the 17th century [2], its practical applications have just recently been investigated. In recent year, it has been demonstrated that fractional-order systems could behave chaotically or hyperchaotically. Examples of such systems include the fractional-order Chua system [3], the fractional-order Chen system [4], the fractional-order hyperchaotic Lorenz system [5], and the fractional-order hyperchaotic Chen system [6]. Nowadays, whereas chaos synchronization of conventional integer-order chaotic and hyperchaotic systems has been extensively studied, chaos synchronization of fractional-order chaotic and hyperchaotic systems is still considered as a challenging research topic. Examples of existing methods for chaos synchronization of fractional-order chaotic and hyperchaotic systems are an active control method [7, 8], a sliding-mode control method [9, 10], a robust control method [11, 12], an adaptive control method [13], and a tracking control-based method [14, 15]. The sliding-mode control, robust control, and adaptive control are commonly used methods to cope with the nonlinear systems that have some uncertain parameters. This paper extends the robust control approach presented in [12] to synchronization of uncertain fractional-order hyperchaotic systems. A unidirectional linear error feedback coupling scheme is adopted here due to its simple configuration and ease of
%U http://www.hindawi.com/journals/jcha/2013/512403/